Stiffness and energy losses in cylindrically symmetric superconductor levitating systems

TL;DR

This paper analyzes the stiffness and hysteretic energy losses in a cylindrically symmetric superconductor-permanent magnet levitating system, considering various parameters to optimize system design.

Contribution

It provides a systematic calculation of stiffness and energy losses considering demagnetization and shape effects using the critical state model.

Findings

Stiffness and energy losses depend on superconductor aspect ratio.

System parameters significantly influence levitation stability.

Design trends for optimizing stiffness and minimizing losses are proposed.

Abstract

Stiffness and hysteretic energy losses are calculated for a magnetically levitating system composed of a type-II superconductor and a permanent magnet when a small vibration is produced in the system. We consider a cylindrically symmetric configuration with only vertical movements and calculate the current profiles under the assumption of the critical state model. The calculations, based on magnetic energy minimization, take into account the demagnetization fields inside the superconductor and the actual shape of the applied field. The dependence of stiffness and hysteretic energy losses upon the different important parameters of the system such as the superconductor aspect ratio, the relative size of the superconductor-permanent magnet, and the critical current of the superconductor are all systematically studied. Finally, in view of the results, we provide some trends on how a system such as the one studied here could be designed in order to optimize both the stiffness and the hysteretic losses.